Standard Form with Interger Coefficients

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Plnrotn

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Jan 13, 2009
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Hi I am "Mom" trying to help her son solve this problem. We are working on Point-Slope Form and have gone through answering the questions in Point-Slope form, Slope-Intercept form, and now we have to answer in standard form with integer coefficients and I am stumped!

I know we need to use the formula Ax+By=C

Problem: (-5,2); m=2/5

My son's attempted answer:

y-2=2/5(x+5)
y-2=2/5x+2
y=2/5x+4

-2/5x+y=4

Is he close?
 


Yes. He's very close.

Multiply both sides of the last equation by -5.

This will "clear" the fraction, leaving all-integer coefficients, and it will lead to A > 0.

If we multiply by positive 5 instead of negative 5, then we will still clear the fraction, but A will end up negative.

Standard form requires that A be greater than zero.

PS: When typing fractional factors, put parentheses around them.

y - 2 = (2/5)(x + 5)

y - 2 = (2/5)x + 2

y = (2/5)x + 4

-(2/5)x + y = 4



EG: (7/24)x - (13/5)y = 9/3

120 is the Least Common Multiple (LCM) of the denominators 24, 5, and 3.

In other words, 120 is the smallest whole number into which 24, 5, and 3 all divide evenly.

Therefore, multiplying both sides of the equation by the LCM 120 will clear all of the fractions.

35x - 312y = 360 is the standard form.

 
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